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 A283477 If 2n = 2^e1 + 2^e2 + ... + 2^ek [e1 .. ek distinct], then a(n) = A002110(e1) * A002110(e2) * ... * A002110(ek). 38
 1, 2, 6, 12, 30, 60, 180, 360, 210, 420, 1260, 2520, 6300, 12600, 37800, 75600, 2310, 4620, 13860, 27720, 69300, 138600, 415800, 831600, 485100, 970200, 2910600, 5821200, 14553000, 29106000, 87318000, 174636000, 30030, 60060, 180180, 360360, 900900, 1801800, 5405400, 10810800, 6306300, 12612600, 37837800, 75675600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = Product of distinct primorials larger than one, obtained as Product_{i} A002110(1+i), where i ranges over the zero-based positions of the 1-bits present in the binary representation of n. This sequence can be represented as a binary tree. Each child to the left is obtained as A283980(k), and each child to the right is obtained as 2*A283980(k), when their parent contains k:                                       1                                       |                    ...................2....................                   6                                       12        30......../ \........60                 180......../ \......360        / \                 / \                 / \                 / \       /   \               /   \               /   \               /   \      /     \             /     \             /     \             /     \   210       420      1260       2520     6300       12600   37800       75600 etc. LINKS Antti Karttunen, Table of n, a(n) for n = 0..4095 FORMULA a(0) = 1; a(2n) = A283980(a(n)), a(2n+1) = 2*A283980(a(n)). Other identities. For all n >= 0 (or for n >= 1): a(2n+1) = 2*a(2n). a(n) = A108951(A019565(n)). A097248(a(n)) = A283475(n). A007814(a(n)) = A051903(a(n)) = A000120(n). A001221(a(n)) = A070939(n). A001222(a(n)) = A029931(n). A048675(a(n)) = A005187(n). A248663(a(n)) = A006068(n). A090880(a(n)) = A283483(n). A276075(a(n)) = A283984(n). A276085(a(n)) = A283985(n). A046660(a(n)) = A124757(n). A056169(a(n)) = A065120(n). [seems to be] A005361(a(n)) = A284001(n). A072411(a(n)) = A284002(n). A007913(a(n)) = A284003(n). A000005(a(n)) = A284005(n). A324286(a(n)) = A324287(n). A276086(a(n)) = A324289(n). A267263(a(n)) = A324341(n). A276150(a(n)) = A324342(n). [subsequences in the latter are converging towards this sequence] G.f.: Product_{k>=0} (1 + prime(k + 1)# * x^(2^k)), where prime()# = A002110. - Ilya Gutkovskiy, Aug 19 2019 MATHEMATICA Table[Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e == 1 :> {Times @@ Prime@ Range@ PrimePi@ p, e}] &[Times @@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[n, 2]], {n, 0, 43}] (* Michael De Vlieger, Mar 18 2017 *) PROG (PARI) A283477(n) = prod(i=0, exponent(n), if(bittest(n, i), vecprod(primes(1+i)), 1)) \\ Edited by M. F. Hasler, Nov 11 2019 (Scheme) (define (A283477 n) (A108951 (A019565 n))) ;; Recursive "binary tree" implementation, using memoization-macro definec: (definec (A283477 n) (cond ((zero? n) 1) ((even? n) (A283980 (A283477 (/ n 2)))) (else (* 2 (A283980 (A283477 (/ (- n 1) 2))))))) (Python) from sympy import prime, primerange, factorint from operator import mul from functools import reduce def P(n): return reduce(mul, [i for i in primerange(2, n + 1)]) def a108951(n):     f = factorint(n)     return 1 if n==1 else reduce(mul, [P(i)**f[i] for i in f]) def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1 # after Chai Wah Wu def a(n): return a108951(a019565(n)) print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 22 2017 CROSSREFS Cf. A129912 (same terms, but sorted into ascending order). Cf. A000120, A001221, A001222, A002110, A005187, A005361, A006068, A007814, A007913, A019565, A029931, A030308, A046660, A048675, A051903, A056169, A065120, A070939, A072411, A090880, A097248, A108951, A124757, A248663, A276075, A276085, A283475, A283483, A283980, A283984, A283985, A284001, A284002, A284003, A284005, A324287, A324289, A324341, A324342, A324343. Cf. A005940, A052330, A322827, A323505 for other similar trees. Cf. also A260443. Sequence in context: A100071 A331552 A129912 * A182863 A161507 A335711 Adjacent sequences:  A283474 A283475 A283476 * A283478 A283479 A283480 KEYWORD nonn AUTHOR Antti Karttunen, Mar 16 2017 EXTENSIONS More formulas and the binary tree illustration added by Antti Karttunen, Mar 19 2017 Four more linking formulas added by Antti Karttunen, Feb 25 2019 STATUS approved

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Last modified April 11 09:24 EDT 2021. Contains 342886 sequences. (Running on oeis4.)